Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [201,4,Mod(5,201)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(201, base_ring=CyclotomicField(22))
chi = DirichletCharacter(H, H._module([11, 5]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("201.5");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 201 = 3 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 201.j (of order \(22\), degree \(10\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(11.8593839112\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{22})\) |
Coefficient field: | \(\Q(\zeta_{33})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - x^{19} + x^{17} - x^{16} + x^{14} - x^{13} + x^{11} - x^{10} + x^{9} - x^{7} + x^{6} - x^{4} + x^{3} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 2^{10}\cdot 3^{10} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{22}]$ |
Embedding invariants
Embedding label | 137.2 | ||
Root | \(0.0475819 + 0.998867i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 201.137 |
Dual form | 201.4.j.a.179.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/201\mathbb{Z}\right)^\times\).
\(n\) | \(68\) | \(136\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{13}{22}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | 0.281733 | − | 0.959493i | \(-0.409091\pi\) | ||||
−0.281733 | + | 0.959493i | \(0.590909\pi\) | |||||||
\(3\) | 5.14326 | + | 0.739490i | 0.989821 | + | 0.142315i | ||||
\(4\) | −6.73003 | − | 4.32513i | −0.841254 | − | 0.540641i | ||||
\(5\) | 0 | 0 | 0.909632 | − | 0.415415i | \(-0.136364\pi\) | ||||
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.34287 | + | 14.7905i | −0.234493 | + | 0.798610i | 0.755211 | + | 0.655482i | \(0.227534\pi\) |
−0.989704 | + | 0.143128i | \(0.954284\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 25.9063 | + | 7.60678i | 0.959493 | + | 0.281733i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | 0.909632 | − | 0.415415i | \(-0.136364\pi\) | ||||
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(12\) | −31.4159 | − | 27.2220i | −0.755750 | − | 0.654861i | ||||
\(13\) | 60.1194 | + | 52.0937i | 1.28262 | + | 1.11140i | 0.987780 | + | 0.155855i | \(0.0498133\pi\) |
0.294844 | + | 0.955545i | \(0.404732\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 26.5866 | + | 58.2164i | 0.415415 | + | 0.909632i | ||||
\(17\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 140.401 | − | 41.2254i | 1.69527 | − | 0.497777i | 0.715622 | − | 0.698487i | \(-0.246143\pi\) |
0.979651 | + | 0.200710i | \(0.0643250\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −33.2739 | + | 72.8597i | −0.345760 | + | 0.757109i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 81.8576 | − | 94.4687i | 0.654861 | − | 0.755750i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 127.618 | + | 58.2811i | 0.909632 | + | 0.415415i | ||||
\(28\) | 93.1983 | − | 80.7568i | 0.629029 | − | 0.545057i | ||||
\(29\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −162.796 | + | 141.063i | −0.943194 | + | 0.817282i | −0.983315 | − | 0.181913i | \(-0.941771\pi\) |
0.0401208 | + | 0.999195i | \(0.487226\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −141.450 | − | 163.242i | −0.654861 | − | 0.755750i | ||||
\(37\) | −257.832 | −1.14561 | −0.572803 | − | 0.819693i | \(-0.694144\pi\) | ||||
−0.572803 | + | 0.819693i | \(0.694144\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 270.687 | + | 312.389i | 1.11140 | + | 1.28262i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | −0.540641 | − | 0.841254i | \(-0.681818\pi\) | ||||
0.540641 | + | 0.841254i | \(0.318182\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 135.200 | + | 210.376i | 0.479485 | + | 0.746093i | 0.993761 | − | 0.111532i | \(-0.0355757\pi\) |
−0.514276 | + | 0.857625i | \(0.671939\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(48\) | 93.6912 | + | 319.083i | 0.281733 | + | 0.959493i | ||||
\(49\) | 88.6527 | + | 56.9736i | 0.258463 | + | 0.166104i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −179.293 | − | 610.616i | −0.478144 | − | 1.62841i | ||||
\(53\) | 0 | 0 | 0.540641 | − | 0.841254i | \(-0.318182\pi\) | ||||
−0.540641 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 752.605 | − | 108.208i | 1.74886 | − | 0.251448i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −42.7885 | − | 19.5409i | −0.0898116 | − | 0.0410156i | 0.370003 | − | 0.929031i | \(-0.379357\pi\) |
−0.459814 | + | 0.888015i | \(0.652084\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −225.016 | + | 350.131i | −0.449989 | + | 0.700196i | ||||
\(64\) | 72.8652 | − | 506.789i | 0.142315 | − | 0.989821i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −40.7384 | + | 546.903i | −0.0742833 | + | 0.997237i | ||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −63.9862 | + | 140.110i | −0.102589 | + | 0.224639i | −0.953966 | − | 0.299916i | \(-0.903041\pi\) |
0.851376 | + | 0.524556i | \(0.175769\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 490.874 | − | 425.345i | 0.755750 | − | 0.654861i | ||||
\(76\) | −1123.21 | − | 329.803i | −1.69527 | − | 0.497777i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1044.95 | − | 905.451i | −1.48817 | − | 1.28951i | −0.858692 | − | 0.512491i | \(-0.828723\pi\) |
−0.629480 | − | 0.777017i | \(-0.716732\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 613.274 | + | 394.127i | 0.841254 | + | 0.540641i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(84\) | 539.062 | − | 346.434i | 0.700196 | − | 0.449989i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1031.58 | + | 662.957i | −1.18834 | + | 0.763701i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −941.617 | + | 605.141i | −1.04990 | + | 0.674733i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 1121.24i | − | 1.17365i | −0.809712 | − | 0.586827i | \(-0.800377\pi\) | ||
0.809712 | − | 0.586827i | \(-0.199623\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −959.493 | + | 281.733i | −0.959493 | + | 0.281733i | ||||
\(101\) | 0 | 0 | −0.281733 | − | 0.959493i | \(-0.590909\pi\) | ||||
0.281733 | + | 0.959493i | \(0.409091\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1333.38 | − | 1538.81i | −1.27556 | − | 1.47207i | −0.809271 | − | 0.587436i | \(-0.800137\pi\) |
−0.466285 | − | 0.884634i | \(-0.654408\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(108\) | −606.798 | − | 944.197i | −0.540641 | − | 0.841254i | ||||
\(109\) | −1129.25 | − | 978.504i | −0.992320 | − | 0.859851i | −0.00218975 | − | 0.999998i | \(-0.500697\pi\) |
−0.990131 | + | 0.140147i | \(0.955242\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1326.10 | − | 190.664i | −1.13394 | − | 0.163037i | ||||
\(112\) | −976.510 | + | 140.401i | −0.823853 | + | 0.118452i | ||||
\(113\) | 0 | 0 | −0.909632 | − | 0.415415i | \(-0.863636\pi\) | ||||
0.909632 | + | 0.415415i | \(0.136364\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1161.21 | + | 1806.87i | 0.917551 | + | 1.42774i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 871.620 | − | 1005.90i | 0.654861 | − | 0.755750i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1705.74 | − | 245.248i | 1.23532 | − | 0.177612i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1818.52 | + | 533.965i | 1.27061 | + | 0.373084i | 0.846433 | − | 0.532496i | \(-0.178746\pi\) |
0.424176 | + | 0.905580i | \(0.360564\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 539.800 | + | 1182.00i | 0.368424 | + | 0.806736i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2255.63i | 1.47059i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | −0.989821 | − | 0.142315i | \(-0.954545\pi\) | ||||
0.989821 | + | 0.142315i | \(0.0454545\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2581.70 | − | 1179.02i | 1.57537 | − | 0.719449i | 0.579918 | − | 0.814675i | \(-0.303085\pi\) |
0.995456 | + | 0.0952257i | \(0.0303573\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 245.920 | + | 1710.41i | 0.142315 | + | 0.989821i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 413.833 | + | 358.588i | 0.232193 | + | 0.201196i | ||||
\(148\) | 1735.22 | + | 1115.16i | 0.963745 | + | 0.619361i | ||||
\(149\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3115.91 | − | 2002.48i | 1.67927 | − | 1.07920i | 0.806106 | − | 0.591771i | \(-0.201571\pi\) |
0.873163 | − | 0.487429i | \(-0.162065\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −470.607 | − | 3273.15i | −0.241530 | − | 1.67988i | ||||
\(157\) | −558.219 | + | 3882.50i | −0.283762 | + | 1.97361i | −0.0646697 | + | 0.997907i | \(0.520599\pi\) |
−0.219093 | + | 0.975704i | \(0.570310\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4158.14 | −1.99810 | −0.999050 | − | 0.0435727i | \(-0.986126\pi\) | ||||
−0.999050 | + | 0.0435727i | \(0.986126\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 587.916 | + | 4089.05i | 0.267600 | + | 1.86120i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3950.86 | 1.76684 | ||||||||
\(172\) | − | 2000.59i | − | 0.886882i | ||||||
\(173\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1041.74 | + | 1620.98i | 0.449989 | + | 0.700196i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | 0.989821 | − | 0.142315i | \(-0.0454545\pi\) | ||||
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 553.132 | − | 3847.12i | 0.227149 | − | 1.57986i | −0.482882 | − | 0.875686i | \(-0.660410\pi\) |
0.710031 | − | 0.704171i | \(-0.248681\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −205.622 | − | 132.145i | −0.0830603 | − | 0.0533796i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1416.23 | + | 1634.42i | −0.545057 | + | 0.629029i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 0.989821 | − | 0.142315i | \(-0.0454545\pi\) | ||||
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(192\) | 749.530 | − | 2552.66i | 0.281733 | − | 0.959493i | ||||
\(193\) | 243.752 | + | 281.305i | 0.0909102 | + | 0.104916i | 0.799382 | − | 0.600823i | \(-0.205160\pi\) |
−0.708472 | + | 0.705739i | \(0.750615\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −350.217 | − | 766.868i | −0.127630 | − | 0.279471i | ||||
\(197\) | 0 | 0 | 0.540641 | − | 0.841254i | \(-0.318182\pi\) | ||||
−0.540641 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3175.15 | − | 932.308i | −1.13106 | − | 0.332108i | −0.337934 | − | 0.941170i | \(-0.609728\pi\) |
−0.793123 | + | 0.609061i | \(0.791546\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −613.957 | + | 2782.74i | −0.215449 | + | 0.976515i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1434.34 | + | 4884.93i | −0.478144 | + | 1.62841i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 497.869 | + | 3462.76i | 0.162440 | + | 1.12979i | 0.894017 | + | 0.448033i | \(0.147875\pi\) |
−0.731577 | + | 0.681759i | \(0.761215\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1379.39 | − | 3020.45i | −0.431517 | − | 0.944891i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −432.708 | + | 673.307i | −0.133515 | + | 0.207753i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 756.046 | + | 5258.41i | 0.227034 | + | 1.57906i | 0.710503 | + | 0.703694i | \(0.248468\pi\) |
−0.483469 | + | 0.875362i | \(0.660623\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2839.23 | − | 1824.66i | 0.841254 | − | 0.540641i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(228\) | −5533.07 | − | 2526.87i | −1.60718 | − | 0.733973i | ||||
\(229\) | 5173.85 | − | 4483.17i | 1.49300 | − | 1.29370i | 0.644370 | − | 0.764714i | \(-0.277120\pi\) |
0.848633 | − | 0.528981i | \(-0.177426\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | 0.989821 | − | 0.142315i | \(-0.0454545\pi\) | ||||
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −4704.86 | − | 5429.70i | −1.28951 | − | 1.48817i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1615.58 | − | 3537.64i | 0.431821 | − | 0.945557i | −0.561206 | − | 0.827676i | \(-0.689663\pi\) |
0.993028 | − | 0.117881i | \(-0.0376101\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2862.78 | + | 2480.61i | 0.755750 | + | 0.654861i | ||||
\(244\) | 203.451 | + | 316.576i | 0.0533796 | + | 0.0830603i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 10588.4 | + | 4835.56i | 2.72763 | + | 1.24567i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | −0.540641 | − | 0.841254i | \(-0.681818\pi\) | ||||
0.540641 | + | 0.841254i | \(0.318182\pi\) | |||||||
\(252\) | 3028.72 | − | 1383.17i | 0.757109 | − | 0.345760i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2682.31 | + | 3095.55i | −0.654861 | + | 0.755750i | ||||
\(257\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1119.73 | − | 3813.46i | 0.268636 | − | 0.914892i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2639.60 | − | 3504.48i | 0.601638 | − | 0.798769i | ||||
\(269\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8212.28 | − | 1180.75i | −1.84081 | − | 0.264669i | −0.868052 | − | 0.496474i | \(-0.834628\pi\) |
−0.972762 | + | 0.231804i | \(0.925537\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −5795.94 | + | 2646.92i | −1.28493 | + | 0.586809i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1049.03 | + | 308.022i | 0.227545 | + | 0.0668132i | 0.393517 | − | 0.919317i | \(-0.371258\pi\) |
−0.165972 | + | 0.986130i | \(0.553076\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5290.48 | + | 2416.08i | −1.13524 | + | 0.518448i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | −0.755750 | − | 0.654861i | \(-0.772727\pi\) | ||||
0.755750 | + | 0.654861i | \(0.227273\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8953.15 | + | 2628.88i | −1.88060 | + | 0.552194i | −0.884230 | + | 0.467052i | \(0.845316\pi\) |
−0.996369 | + | 0.0851419i | \(0.972866\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2040.93 | − | 4469.02i | 0.415415 | − | 0.909632i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 829.143 | − | 5766.82i | 0.167028 | − | 1.16171i | ||||
\(292\) | 1036.62 | − | 666.198i | 0.207753 | − | 0.133515i | ||||
\(293\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −5143.26 | + | 739.490i | −0.989821 | + | 0.142315i | ||||
\(301\) | −3698.71 | + | 1086.04i | −0.708273 | + | 0.207968i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 6132.78 | + | 7077.60i | 1.15704 | + | 1.33529i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6424.56 | − | 7414.33i | −1.19436 | − | 1.37837i | −0.907316 | − | 0.420449i | \(-0.861873\pi\) |
−0.287045 | − | 0.957917i | \(-0.592673\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5720.01 | − | 8900.52i | −1.05308 | − | 1.63862i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.540641 | − | 0.841254i | \(-0.681818\pi\) | ||||
0.540641 | + | 0.841254i | \(0.318182\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7292.09 | + | 1048.44i | −1.31685 | + | 0.189334i | −0.764686 | − | 0.644403i | \(-0.777106\pi\) |
−0.552161 | + | 0.833737i | \(0.686197\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3116.33 | + | 10613.2i | 0.554769 | + | 1.88937i | ||||
\(317\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −2422.70 | − | 5304.97i | −0.415415 | − | 0.909632i | ||||
\(325\) | 9842.46 | − | 1415.13i | 1.67988 | − | 0.241530i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −5084.46 | − | 5867.78i | −0.859851 | − | 0.992320i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1454.39 | + | 2263.08i | −0.241512 | + | 0.375800i | −0.940757 | − | 0.339082i | \(-0.889884\pi\) |
0.699245 | + | 0.714883i | \(0.253520\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −6679.49 | − | 1961.27i | −1.09920 | − | 0.322754i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −5126.27 | −0.832325 | ||||||||
\(337\) | 1044.04 | − | 3555.66i | 0.168761 | − | 0.574746i | −0.831067 | − | 0.556173i | \(-0.812269\pi\) |
0.999827 | − | 0.0185734i | \(-0.00591244\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5223.55 | + | 4526.23i | −0.822289 | + | 0.712518i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | −0.755750 | − | 0.654861i | \(-0.772727\pi\) | ||||
0.755750 | + | 0.654861i | \(0.227273\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8360.54 | − | 5372.99i | −1.28232 | − | 0.824097i | −0.291148 | − | 0.956678i | \(-0.594037\pi\) |
−0.991172 | + | 0.132581i | \(0.957673\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4636.22 | + | 10151.9i | 0.705024 | + | 1.54379i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | 0.540641 | − | 0.841254i | \(-0.318182\pi\) | ||||
−0.540641 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12242.7 | − | 7867.92i | 1.78491 | − | 1.14709i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5226.82 | − | 4529.07i | 0.755750 | − | 0.654861i | ||||
\(364\) | 9809.94 | 1.41258 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9407.20 | − | 1352.55i | 1.33802 | − | 0.192378i | 0.564121 | − | 0.825692i | \(-0.309215\pi\) |
0.773895 | + | 0.633314i | \(0.218306\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 8954.42 | 1.24802 | ||||||||
\(373\) | 10598.9i | 1.47129i | 0.677366 | + | 0.735646i | \(0.263121\pi\) | ||||
−0.677366 | + | 0.735646i | \(0.736879\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13793.5 | + | 1983.20i | 1.86945 | + | 0.268787i | 0.981544 | − | 0.191236i | \(-0.0612496\pi\) |
0.887907 | + | 0.460022i | \(0.152159\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8958.25 | + | 4091.10i | 1.20458 | + | 0.550113i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | −0.281733 | − | 0.959493i | \(-0.590909\pi\) | ||||
0.281733 | + | 0.959493i | \(0.409091\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1902.26 | + | 6478.50i | 0.249864 | + | 0.850957i | ||||
\(388\) | −4849.49 | + | 7545.96i | −0.634525 | + | 0.987340i | ||||
\(389\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3958.90 | − | 8668.78i | −0.500482 | − | 1.09590i | −0.976312 | − | 0.216366i | \(-0.930580\pi\) |
0.475830 | − | 0.879537i | \(-0.342148\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1668.02 | + | 11601.3i | −0.209286 | + | 1.45562i | ||||
\(400\) | 7675.94 | + | 2253.86i | 0.959493 | + | 0.281733i | ||||
\(401\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −17135.7 | −2.11809 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3791.68 | − | 12913.3i | 0.458403 | − | 1.56118i | −0.328749 | − | 0.944417i | \(-0.606627\pi\) |
0.787152 | − | 0.616759i | \(-0.211555\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2318.18 | + | 16123.3i | 0.277205 | + | 1.92800i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 14150.2 | − | 4154.88i | 1.66173 | − | 0.487927i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12350.9 | + | 3626.56i | −1.42980 | + | 0.419828i | −0.902809 | − | 0.430041i | \(-0.858499\pi\) |
−0.526994 | + | 0.849869i | \(0.676681\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 474.843 | − | 547.999i | 0.0538157 | − | 0.0621066i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(432\) | 8978.95i | 1.00000i | ||||||||
\(433\) | 10305.1 | − | 8929.45i | 1.14373 | − | 0.991044i | 0.143727 | − | 0.989617i | \(-0.454091\pi\) |
0.999999 | − | 0.00142668i | \(-0.000454128\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3367.76 | + | 11469.5i | 0.369923 | + | 1.25984i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −18370.0 | −1.99716 | −0.998580 | − | 0.0532736i | \(-0.983034\pi\) | ||||
−0.998580 | + | 0.0532736i | \(0.983034\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1863.28 | + | 2150.34i | 0.201196 | + | 0.232193i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | −0.540641 | − | 0.841254i | \(-0.681818\pi\) | ||||
0.540641 | + | 0.841254i | \(0.318182\pi\) | |||||||
\(444\) | 8100.04 | + | 7018.73i | 0.865791 | + | 0.750212i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 7179.19 | + | 3278.63i | 0.757109 | + | 0.345760i | ||||
\(449\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 17506.8 | − | 7995.08i | 1.81576 | − | 0.829231i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10724.1 | − | 12376.3i | 1.09771 | − | 1.26682i | 0.136604 | − | 0.990626i | \(-0.456381\pi\) |
0.961102 | − | 0.276194i | \(-0.0890732\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7164.31 | + | 3271.83i | 0.719122 | + | 0.328412i | 0.741145 | − | 0.671345i | \(-0.234283\pi\) |
−0.0220224 | + | 0.999757i | \(0.507011\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(468\) | − | 17182.7i | − | 1.69716i | ||||||
\(469\) | −7912.03 | − | 2977.67i | −0.778985 | − | 0.293169i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5742.13 | + | 19555.9i | −0.561748 | + | 1.91314i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7598.37 | − | 16638.1i | 0.733973 | − | 1.60718i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −15500.7 | − | 13431.5i | −1.46938 | − | 1.27323i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10216.7 | + | 2999.89i | −0.959493 | + | 0.281733i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8391.85 | + | 13058.0i | −0.780844 | + | 1.21502i | 0.191506 | + | 0.981491i | \(0.438663\pi\) |
−0.972351 | + | 0.233526i | \(0.924974\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −21386.4 | − | 3074.90i | −1.97776 | − | 0.284359i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −12540.4 | − | 5727.01i | −1.13524 | − | 0.518448i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 22157.7i | 1.98781i | 0.110258 | + | 0.993903i | \(0.464832\pi\) | ||||
−0.110258 | + | 0.993903i | \(0.535168\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | −0.281733 | − | 0.959493i | \(-0.590909\pi\) | ||||
0.281733 | + | 0.959493i | \(0.409091\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 21465.8i | 1.88034i | ||||||||
\(508\) | −9929.21 | − | 11458.9i | −0.867199 | − | 1.00080i | ||||
\(509\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1794.41 | − | 1554.87i | −0.155343 | − | 0.134605i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 20320.3 | + | 2921.62i | 1.74886 | + | 0.251448i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 1479.42 | − | 10289.6i | 0.126216 | − | 0.877855i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | −0.281733 | − | 0.959493i | \(-0.590909\pi\) | ||||
0.281733 | + | 0.959493i | \(0.409091\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3751.57 | − | 4329.54i | 0.313661 | − | 0.361984i | −0.576927 | − | 0.816796i | \(-0.695748\pi\) |
0.890587 | + | 0.454812i | \(0.150294\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4159.24 | + | 9107.47i | 0.345760 | + | 0.757109i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11674.2 | − | 3427.84i | −0.959493 | − | 0.281733i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 9755.89 | − | 15180.5i | 0.795059 | − | 1.23714i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2802.54 | + | 1279.88i | −0.222718 | + | 0.101712i | −0.523649 | − | 0.851934i | \(-0.675430\pi\) |
0.300931 | + | 0.953646i | \(0.402703\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5689.81 | − | 19377.7i | 0.449674 | − | 1.53145i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18732.8 | − | 8554.98i | 1.46427 | − | 0.668711i | 0.485608 | − | 0.874177i | \(-0.338598\pi\) |
0.978664 | + | 0.205466i | \(0.0658710\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −959.850 | − | 831.714i | −0.0746182 | − | 0.0646570i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 17930.1 | − | 11523.0i | 1.37878 | − | 0.886088i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −22474.3 | − | 3231.32i | −1.71425 | − | 0.246472i | ||||
\(557\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2831.10 | + | 19690.7i | −0.214209 | + | 1.48986i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | −0.909632 | − | 0.415415i | \(-0.863636\pi\) | ||||
0.909632 | + | 0.415415i | \(0.136364\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −8492.69 | + | 7358.96i | −0.629029 | + | 0.545057i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2470.41 | + | 17182.1i | 0.181057 | + | 1.25928i | 0.854270 | + | 0.519829i | \(0.174004\pi\) |
−0.673214 | + | 0.739448i | \(0.735087\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 5742.70 | − | 12574.8i | 0.415415 | − | 0.909632i | ||||
\(577\) | −13498.9 | − | 21004.7i | −0.973945 | − | 1.51549i | −0.852393 | − | 0.522902i | \(-0.824849\pi\) |
−0.121552 | − | 0.992585i | \(-0.538787\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1045.66 | + | 1627.08i | 0.0750537 | + | 0.116786i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | 0.909632 | − | 0.415415i | \(-0.136364\pi\) | ||||
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(588\) | −1234.17 | − | 4203.19i | −0.0865582 | − | 0.294790i | ||||
\(589\) | −17041.3 | + | 26516.8i | −1.19215 | + | 1.85502i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −6854.88 | − | 15010.1i | −0.475902 | − | 1.04208i | ||||
\(593\) | 0 | 0 | 0.989821 | − | 0.142315i | \(-0.0454545\pi\) | ||||
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −15641.2 | − | 7143.10i | −1.07228 | − | 0.489694i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 0.540641 | − | 0.841254i | \(-0.318182\pi\) | ||||
−0.540641 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8958.34 | − | 2630.41i | −0.608017 | − | 0.178530i | −0.0367916 | − | 0.999323i | \(-0.511714\pi\) |
−0.571226 | + | 0.820793i | \(0.693532\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5215.55 | + | 13858.4i | −0.352228 | + | 0.935914i | ||||
\(604\) | −29631.2 | −1.99615 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 20730.6 | + | 13322.7i | 1.38621 | + | 0.890863i | 0.999509 | − | 0.0313428i | \(-0.00997836\pi\) |
0.386701 | + | 0.922205i | \(0.373615\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3996.21 | − | 27794.3i | −0.263304 | − | 1.83132i | −0.507566 | − | 0.861613i | \(-0.669455\pi\) |
0.244262 | − | 0.969709i | \(-0.421454\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10431.6 | − | 22842.0i | −0.677353 | − | 1.48320i | −0.865424 | − | 0.501040i | \(-0.832951\pi\) |
0.188072 | − | 0.982155i | \(-0.439776\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −10989.6 | + | 24063.8i | −0.705024 | + | 1.54379i | ||||
\(625\) | −2223.67 | − | 15466.0i | −0.142315 | − | 0.989821i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 20549.1 | − | 23714.9i | 1.30573 | − | 1.50689i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1988.19 | + | 1722.77i | −0.125433 | + | 0.108689i | −0.715319 | − | 0.698798i | \(-0.753718\pi\) |
0.589885 | + | 0.807487i | \(0.299173\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 18178.0i | 1.14141i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2361.78 | + | 8043.47i | 0.146903 | + | 0.500304i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −11300.0 | + | 24743.5i | −0.693044 | + | 1.51755i | 0.155163 | + | 0.987889i | \(0.450410\pi\) |
−0.848207 | + | 0.529665i | \(0.822318\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | −0.989821 | − | 0.142315i | \(-0.954545\pi\) | ||||
0.989821 | + | 0.142315i | \(0.0454545\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4860.99 | − | 16555.0i | −0.292653 | − | 0.996685i | ||||
\(652\) | 27984.4 | + | 17984.5i | 1.68091 | + | 1.08025i | ||||
\(653\) | 0 | 0 | −0.540641 | − | 0.841254i | \(-0.681818\pi\) | ||||
0.540641 | + | 0.841254i | \(0.318182\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2723.43 | + | 3143.01i | −0.161722 | + | 0.186637i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3308.86 | − | 11268.9i | 0.194705 | − | 0.663103i | −0.803037 | − | 0.595930i | \(-0.796784\pi\) |
0.997741 | − | 0.0671734i | \(-0.0213981\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 27604.5i | 1.59529i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11244.5 | + | 1616.72i | 0.644048 | + | 0.0926001i | 0.456597 | − | 0.889674i | \(-0.349068\pi\) |
0.187451 | + | 0.982274i | \(0.439977\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 15952.2 | − | 7285.14i | 0.909632 | − | 0.415415i | ||||
\(676\) | 13729.0 | − | 30062.2i | 0.781120 | − | 1.71041i | ||||
\(677\) | 0 | 0 | 0.281733 | − | 0.959493i | \(-0.409091\pi\) | ||||
−0.281733 | + | 0.959493i | \(0.590909\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 16583.6 | + | 4869.39i | 0.937291 | + | 0.275214i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | −0.755750 | − | 0.654861i | \(-0.772727\pi\) | ||||
0.755750 | + | 0.654861i | \(0.227273\pi\) | |||||||
\(684\) | −26589.4 | − | 17088.0i | −1.48636 | − | 0.955227i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 29925.7 | − | 19232.1i | 1.66192 | − | 1.06805i | ||||
\(688\) | −8652.81 | + | 13464.0i | −0.479485 | + | 0.746093i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14600.7 | + | 31971.0i | −0.803813 | + | 1.76011i | −0.171826 | + | 0.985127i | \(0.554967\pi\) |
−0.631988 | + | 0.774978i | \(0.717761\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | − | 15414.9i | − | 0.832325i | ||||||
\(701\) | 0 | 0 | 0.755750 | − | 0.654861i | \(-0.227273\pi\) | ||||
−0.755750 | + | 0.654861i | \(0.772727\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −36199.9 | + | 10629.3i | −1.94211 | + | 0.570256i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10441.7 | − | 12050.4i | −0.553099 | − | 0.638311i | 0.408503 | − | 0.912757i | \(-0.366051\pi\) |
−0.961602 | + | 0.274446i | \(0.911505\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −20183.1 | − | 31405.6i | −1.06459 | − | 1.65654i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 28550.4 | − | 13038.5i | 1.47472 | − | 0.673482i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 10925.4 | − | 17000.3i | 0.561993 | − | 0.874478i | ||||
\(724\) | −20361.9 | + | 23498.8i | −1.04522 | + | 1.20625i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 25617.7 | − | 3683.27i | 1.30689 | − | 0.187902i | 0.546549 | − | 0.837427i | \(-0.315941\pi\) |
0.760341 | + | 0.649524i | \(0.225032\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 12889.6 | + | 14875.4i | 0.654861 | + | 0.755750i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 812.298 | + | 1778.69i | 0.0410156 | + | 0.0898116i | ||||
\(733\) | −16759.1 | + | 26077.7i | −0.844492 | + | 1.31406i | 0.103132 | + | 0.994668i | \(0.467114\pi\) |
−0.947624 | + | 0.319388i | \(0.896523\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1169.23 | + | 3982.03i | −0.0582014 | + | 0.198216i | −0.983461 | − | 0.181118i | \(-0.942029\pi\) |
0.925260 | + | 0.379333i | \(0.123847\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 50883.1 | + | 32700.6i | 2.52259 | + | 1.62117i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1212.12 | − | 778.981i | −0.0588959 | − | 0.0378501i | 0.510862 | − | 0.859663i | \(-0.329326\pi\) |
−0.569757 | + | 0.821813i | \(0.692963\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 16600.4 | − | 4874.30i | 0.798610 | − | 0.234493i | ||||
\(757\) | 38953.7 | + | 5600.70i | 1.87027 | + | 0.268905i | 0.981785 | − | 0.189993i | \(-0.0608465\pi\) |
0.888489 | + | 0.458898i | \(0.151756\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 19376.7 | − | 12452.7i | 0.919377 | − | 0.590848i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −16085.0 | + | 13937.7i | −0.755750 | + | 0.654861i | ||||
\(769\) | −24038.3 | + | 3456.19i | −1.12724 | + | 0.162072i | −0.680608 | − | 0.732648i | \(-0.738284\pi\) |
−0.446627 | + | 0.894720i | \(0.647375\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −423.779 | − | 2947.45i | −0.0197567 | − | 0.137411i | ||||
\(773\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 26926.2i | 1.24802i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 8579.10 | − | 18785.6i | 0.396105 | − | 0.867349i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −959.832 | + | 6675.78i | −0.0437241 | + | 0.304108i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 20613.7 | + | 32075.5i | 0.933670 | + | 1.45282i | 0.891142 | + | 0.453724i | \(0.149905\pi\) |
0.0425282 | + | 0.999095i | \(0.486459\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1554.46 | − | 3403.80i | −0.0696098 | − | 0.152424i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 17336.5 | + | 20007.4i | 0.771955 | + | 0.890883i | ||||
\(797\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 16167.7 | − | 16072.5i | 0.709191 | − | 0.705016i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | 0.909632 | − | 0.415415i | \(-0.136364\pi\) | ||||
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −12840.0 | + | 43729.1i | −0.555948 | + | 1.89338i | −0.121767 | + | 0.992559i | \(0.538856\pi\) |
−0.434181 | + | 0.900826i | \(0.642962\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −41364.8 | − | 12145.8i | −1.78441 | − | 0.523950i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 27655.1 | + | 23963.3i | 1.18425 | + | 1.02615i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −31767.4 | + | 9327.76i | −1.35536 | + | 0.397971i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1079.75 | + | 317.043i | −0.0457323 | + | 0.0134282i | −0.304519 | − | 0.952506i | \(-0.598496\pi\) |
0.258786 | + | 0.965935i | \(0.416677\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 25186.1 | − | 29066.3i | 1.05519 | − | 1.21775i | 0.0798996 | − | 0.996803i | \(-0.474540\pi\) |
0.975286 | − | 0.220946i | \(-0.0709145\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5167.65 | + | 2359.98i | 0.215720 | + | 0.0985162i | ||||
\(832\) | 30781.1 | − | 26672.0i | 1.28262 | − | 1.11140i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −28997.0 | + | 8514.29i | −1.19747 | + | 0.351609i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 24389.0 | 1.00000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 11626.2 | − | 25457.8i | 0.474159 | − | 1.03826i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 11092.4 | + | 17260.2i | 0.449989 | + | 0.700196i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −47992.4 | + | 6900.27i | −1.94004 | + | 0.278936i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 14661.3 | + | 9422.23i | 0.588502 | + | 0.378207i | 0.800741 | − | 0.599010i | \(-0.204439\pi\) |
−0.212239 | + | 0.977218i | \(0.568076\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | 0.540641 | − | 0.841254i | \(-0.318182\pi\) | ||||
−0.540641 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 32943.2 | − | 38018.4i | 1.30851 | − | 1.51010i | 0.621699 | − | 0.783256i | \(-0.286443\pi\) |
0.686807 | − | 0.726840i | \(-0.259012\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 13801.9 | − | 21476.1i | 0.540641 | − | 0.841254i | ||||
\(868\) | −3780.47 | + | 26293.7i | −0.147831 | + | 1.02819i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −30939.4 | + | 30757.3i | −1.20361 | + | 1.19652i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 8529.00 | − | 29047.1i | 0.330656 | − | 1.12611i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 5824.28 | − | 2659.86i | 0.224639 | − | 0.102589i | ||||
\(877\) | 18405.6 | − | 40302.6i | 0.708680 | − | 1.55179i | −0.120438 | − | 0.992721i | \(-0.538430\pi\) |
0.829119 | − | 0.559073i | \(-0.188843\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 20657.2 | + | 17899.6i | 0.787284 | + | 0.682185i | 0.952657 | − | 0.304046i | \(-0.0983376\pi\) |
−0.165374 | + | 0.986231i | \(0.552883\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −15795.2 | + | 24577.8i | −0.595898 | + | 0.927235i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 17655.1 | − | 38659.3i | 0.662709 | − | 1.45113i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −27000.0 | −1.00000 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −19826.6 | + | 2850.63i | −0.730661 | + | 0.105053i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −30788.3 | − | 35531.6i | −1.12713 | − | 1.30078i | −0.948469 | − | 0.316871i | \(-0.897368\pi\) |
−0.178665 | − | 0.983910i | \(-0.557178\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(912\) | 26308.7 | + | 40937.1i | 0.955227 | + | 1.48636i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −54210.5 | + | 7794.29i | −1.95542 | + | 0.281147i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −5806.85 | − | 19776.3i | −0.208434 | − | 0.709860i | −0.995649 | − | 0.0931816i | \(-0.970296\pi\) |
0.787216 | − | 0.616678i | \(-0.211522\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −27560.4 | − | 42884.8i | −0.986042 | − | 1.53431i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −21105.5 | + | 24357.1i | −0.750212 | + | 0.865791i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −22837.7 | − | 50007.6i | −0.809157 | − | 1.77181i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | 0.281733 | − | 0.959493i | \(-0.409091\pi\) | ||||
−0.281733 | + | 0.959493i | \(0.590909\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 14795.7 | + | 4344.41i | 0.520848 | + | 0.152935i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 17841.3i | 0.622039i | 0.950404 | + | 0.311020i | \(0.100670\pi\) | ||||
−0.950404 | + | 0.311020i | \(0.899330\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −38280.4 | −1.33039 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | −0.989821 | − | 0.142315i | \(-0.954545\pi\) | ||||
0.989821 | + | 0.142315i | \(0.0454545\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(948\) | 8179.71 | + | 56891.1i | 0.280237 | + | 1.94909i | ||||
\(949\) | −11145.7 | + | 5090.06i | −0.381248 | + | 0.174110i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2363.91 | − | 16441.3i | 0.0793497 | − | 0.551889i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −26173.7 | + | 16820.8i | −0.874478 | + | 0.561993i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −40169.2 | −1.33584 | −0.667918 | − | 0.744234i | \(-0.732815\pi\) | ||||
−0.667918 | + | 0.744234i | \(0.732815\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(972\) | −8537.61 | − | 29076.4i | −0.281733 | − | 0.959493i | ||||
\(973\) | 6226.30 | + | 43304.9i | 0.205145 | + | 1.42681i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 51668.8 | 1.69716 | ||||||||
\(976\) | − | 3010.52i | − | 0.0987340i | ||||||
\(977\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −21811.5 | − | 33939.4i | −0.709877 | − | 1.10459i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | 0.989821 | − | 0.142315i | \(-0.0454545\pi\) | ||||
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −50345.8 | − | 78339.7i | −1.62117 | − | 2.52259i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 31996.9 | − | 49788.2i | 1.02565 | − | 1.59594i | 0.246450 | − | 0.969155i | \(-0.420736\pi\) |
0.779196 | − | 0.626781i | \(-0.215628\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −9153.84 | + | 10564.1i | −0.292536 | + | 0.337604i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 33560.1 | + | 38730.5i | 1.06606 | + | 1.23030i | 0.972062 | + | 0.234725i | \(0.0754189\pi\) |
0.0939968 | + | 0.995572i | \(0.470036\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −32904.0 | − | 15026.8i | −1.04208 | − | 0.475902i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 201.4.j.a.137.2 | ✓ | 20 | |
3.2 | odd | 2 | CM | 201.4.j.a.137.2 | ✓ | 20 | |
67.45 | odd | 22 | inner | 201.4.j.a.179.2 | yes | 20 | |
201.179 | even | 22 | inner | 201.4.j.a.179.2 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
201.4.j.a.137.2 | ✓ | 20 | 1.1 | even | 1 | trivial | |
201.4.j.a.137.2 | ✓ | 20 | 3.2 | odd | 2 | CM | |
201.4.j.a.179.2 | yes | 20 | 67.45 | odd | 22 | inner | |
201.4.j.a.179.2 | yes | 20 | 201.179 | even | 22 | inner |